Rye now won't hurt a thing. Rye after you have bermuda in will definitely weaken the bermuda in the spring...unless you have the special spray herbicide that only golf courses can buy. Bermuda must have full sun to thrive. When you have all that ryegrass growing above it in the spring, the bermuda never awakens. But bermuda is bermuda. Once the rye dies off the bermuda will come back after it gets really hot in May and June. But by then the fact that it was thin for so long will allow weeds to get in. So it becomes one herbicidal cocktail after another to get it right and keep it going. It is much better to let it go dormant and take what you get. Having said that, I see bermuda lawns every year that never go dormant in the winter. The owners continue to water weekly and fertilize all winter long and the grass remains green. Las Vegas gets colder in the high desert than we do, but you might be able to extend your growing season simply with water and fertilizer.

Don't dig out the rye next spring. Just use RoundUp and kill it. You can't just use RU on bermuda, though, because it kills everything.

The people recommending planting rye are probably selling lawn mowers, sprinklers, or fertilizer.

Find the Bermuda Bible online and memorize it. I would only add to that guide a suggestion to fertilize at least one time per year with any organic fertilizer. If you never use organic fertilizer, it can happen that your turf will crash due to poor health of the microbes in the soil. Organic fertilizer is food for those microbes.